Problem: What do the following two equations represent? $5x-5y = -1$ $25x+25y = 4$
Explanation: Putting the first equation in $y = mx + b$ form gives: $5x-5y = -1$ $-5y = -5x-1$ $y = 1x + \dfrac{1}{5}$ Putting the second equation in $y = mx + b$ form gives: $25x+25y = 4$ $25y = -25x+4$ $y = -1x + \dfrac{4}{25}$ The slopes are negative inverses of each other, so the lines are perpendicular.